A note on generalized convexity for fuzzy mappings through a linear ordering

In this paper, we study generalized convexity for fuzzy mappings that are defined through a linear ordering on the space of fuzzy intervals. On top of the concepts of convexity, preinvexity and prequasiinvexity, which have been introduced previously by other authors, we now introduce the concept of...

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Bibliographic Details
Published in:Fuzzy sets and systems 2013-11, Vol.231, p.70-83
Main Authors: Chalco-Cano, Y., Rufián-Lizana, A., Román-Flores, H., Osuna-Gómez, R.
Format: Article
Language:English
Subjects:
Convexity
Derivatives
Differentiable fuzzy mappings
Fuzzy
Fuzzy generalized convexity
Fuzzy logic
Fuzzy optimization
Fuzzy set theory
Intervals
Mapping
Order disorder
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Summary:In this paper, we study generalized convexity for fuzzy mappings that are defined through a linear ordering on the space of fuzzy intervals. On top of the concepts of convexity, preinvexity and prequasiinvexity, which have been introduced previously by other authors, we now introduce the concept of invex fuzzy mappings. For this purpose, we first consider the notion of strongly generalized differentiability for fuzzy mappings and we establish new properties thereof. Then, we introduce the ith strongly generalized partial derivative of a fuzzy function. After that, we present new characterizations for convex and invex fuzzy mappings. Finally, we study local-global minimum properties for convex and invex fuzzy mappings.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2013.07.001